code: def _do_step(
      x, y, z, tau, kappa, d_x, d_y, d_z, d_tau, d_kappa, alpha
  ):
      """
      An implementation of [4] Equation 8.9
  
      References
      ----------
      .. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
             optimizer for linear programming: an implementation of the
             homogeneous algorithm." High performance optimization. Springer US,
             2000. 197-232.
  
      """
      x = x + alpha * d_x
      tau = tau + alpha * d_tau
      z = z + alpha * d_z
      kappa = kappa + alpha * d_kappa
      y = y + alpha * d_y
      return x, y, z, tau, kappa
  
file_path: scipy/scipy/optimize/_linprog_ip.py
imports: import numpy
  import scipy
  import scipy.sparse
  from warnings import warn
  from scipy.linalg import LinAlgError
  from ._optimize import OptimizeWarning, OptimizeResult, _check_unknown_options
  from ._linprog_util import _postsolve
label_desc: Use image node_id 6 for calling a global function with example usage: _do_step(x, y, z, tau, kappa, d_x, d_y, d_z, d_tau, d_kappa, alpha) and returns: x,  y,  z,  tau,  kappa